Liquid metal MHD flow in a duct whose cross section changes from a rectangle to a trapezoid

This paper treats the liquid-metal MHD flow in a semi-infinite rectangular duct and a semi-infinite trapezoidal duct, which are connected by a finite-length transition duct. There is a strong, transverse, uniform magnetic field. The walls parallel to the magnetic field (sides) remain parallel, while the walls intersecting the magnetic field are twisted in the transition duct to provide the change in cross-sectional shape. The left side has a constant height, while the height of the right side increases or decreases in the transition duct. This geometry gives a skewed velocity profile with a high velocity near the left side, provided that the right side is relatively thick. All walls are thin and electrically conducting, but the sides are considerably thicker than the other walls. Junctions of different ducts with walls parallel to the magnetic field are treated for the first time. In expansions, contractions and other geometric transition ducts, as well as in straight ducts with axially varying magnetic fields, the fluid flow and the electric currents are concentrated in boundary layers adjacent to the sides and in the sides. At a junction with a straight duct with a uniform magnetic field, the flow and current must transfer from the boundary layers and sides to the core regions. These transfers at junctions play a key role in any three-dimensional flow.     

Hall effect on MHD flow and heat transfer over a stretching sheet with variable thickness

We investigate the MHD flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness. The wall temperature and the wall velocity are assumed to vary. The effects of external magnetic field along the sheet and the Hall currents are considered. The governing equations are solved numerically using an implicit finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in very good agreement. The effects of the physical parameters on the velocity and temperature fields are presented graphically and analyzed. The effect of the Hall current gives rise to a cross flow. Moreover, the Hall current and the magnetic field have strong effect on the flow and heat transfer characteristics, i.e., shear stress and the Nusselt number.     

Hall effects on combined free and forced convective hydromagnetic flow through a channel

Hydromagnetic free and forced convection in a parallel plate channel permeated by a transverse magnetic field has been considered taking Hall effects into account. When there is a uniform axial temperature variation along the walls, the primary flow shows incipient flow reversal at the upper plate for an increase in temperature along that plate. Similarly flow reversal at the lower plate occurs for a decrease in temperature along that plate. Hall currents are found to exert a destabilizing influence on the flow. The skin-friction for the cross-flow increases with the Hall parameter. The induced magnetic field and the heat transfer characteristics in the flow are also determined.     

Hall effects on magnetohydrodynamic free convection about a semi-infinite vertical flat plate

A theoretical analysis is presented for the problem of free convection flow of a conducting fluid along a semi-infinite vertical flat plate when the fluid is permeated by a transverse magnetic field and the Hall effects are taken into account. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by employing the difference-differential method in combination with the Simpson's rule. The velocity and temperature profiles as well as the local Nusselt number are computed for various values of the Hall and magnetic parameters. The results are compared with those known from the literature.     

Evaluation of the Hall parameter of electrolyte solutions in thermosyphonic MHD flow

The objective of this work is to determine experimentally the Hall parameter of electrolyte solutions using a closed loop thermosyphonic magnetohydrodynamic flow. The upper and lower parts of the loop, which represent the heat sink and heat source of the system respectively, are constructed from copper pipe coated with varnish on the inside surface. The middle region, connecting the upper and lower parts of the loop, is made from plastic vertical pipes, with segmented copper electrodes placed vertically opposite to each other on each side of the loop plastic walls and connected as a Hall generator to measure the open circuit voltage. A transverse magnetic field is imposed in the middle non-conducting plastic-wall region by a set of permanent magnets. The magnets provide a magnetic field strength of up to 0.225 T, whereas the driving temperature difference between the hot and cold portion of the loop ranges from 10 to 80 °C. Measurements of the induced flow rate and induced open circuit voltage are reported as a function of driving temperature difference and magnetic field strength.The analytical one-dimensional model of Ghaddar [Int. J. Heat Mass Transfer 41 (8-9) (1998) 1075] is extended to account for the electrode design and the Hall effect pertinent to electrolyte solutions. The open circuit voltage is related to the driving temperature difference, flow characteristic, magnetic field strength, electrolyte electric properties and electrode design. The developed 1-D model and the measured open circuit voltage are used to evaluate the Hall parameter (ωτ), which is a property of the fluid of the electrolyte liquid. It is found that ωτ can be as large as 100 for electrolytes and causes a significant loss in power output at the electrodes due to electron drift in the fluid leading to generation of current in an axial direction at the expense of the current flowing in the transverse direction between the electrodes.     

Conjugated heat and electrophysical characteristics of K-phase films on electrode walls of the channel of an aluminum-hydrogen MHD generator at high thermal and electric parameters

The utilization of aluminum as an intermediate energy carrier with subsequent production of high-temperature hydrogen in reactions of hydrothermal oxidation makes it possible to build high-performance thermal-power cycles with an MHD generator, with a real prospect for their utilization in emergency and high-peak power plants [1]. One of the main problems of efficient operation of an MHD generator channel is the deposition of K-phase in the form of conducting melt films of Al₂O₃ on the fire surface of MHDG channel walls. As this takes place, there are leakage currents through the melt films in the induced transversal and Hall fields, which are accompanied by Joule heat-evolution. The peculiarities of formation, flow, and thermal regime of such a film on the fire walls of MHDGs in the induced Hall and transversal fields were studied in this connection, as well as the peculiarities of current flow with regard to temperature dependencies of the conduction and the viscosity of the Al₂O₃ melt. The results of investigation make it possible to estimate the influence of such films on aluminum-hydrogen MHDG performance.     

Radiation and thermal diffusion effects on an unsteady MHD free convection mass-transfer flow past an infinite vertical porous plate with the hall current and a heat source

An analysis is performed to study the effects of radiation and thermal diffusion on an unsteady MHD free convection heat- and mass-transfer flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate with the Hall current and a heat source. The flow is considered under the influence of a constant suction velocity and a uniform magnetic field applied normally to the flow. The dimensionless governing equations are solved numerically by the Galerkin finite element method. The effects of the flow parameters on the primary and secondary velocities, temperature, species concentration, shearing stresses, Nusselt number, and Sherwood number are calculated and presented in figures and tables. The results obtained show that a decrease in the temperature boundary layer thickness occurs when the Prandtl number and radiation parameter are increased and an increase in the Schmidt number leads to a decrease in the concentration boundary layer thickness.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.     

Magnetohydrodynamic flow in a rectangular duct with suction and injection

Summary The effects of suction or injection on an incompressible laminar flow in a rectangular duct with nonconducting walls in the presence of an imposed transverse magnetic field are examined. Analytical solutions are obtained for the velocity and magnetic field, which are useful for obtaining the current density and electric field strength.     

Effects of Hall current and two temperatures in transversely isotropic magnetothermoelastic with and without energy dissipation due to ramp-type heat

The present article is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of type-II and type-III. Laplace and Fourier transform techniques are applied to solve the problem. The analytical expressions of displacements, stress components, temperature change, and current density components are obtained in the transformed domain. A numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of Hall current and two temperatures on resulting quantities. Some special cases are also deduced from the present investigation.     

Hall effects on free and forced convective flow in a rotating channel

Summary The influence of Hall currents on the free and forced convective flow of a viscous rotating fluid between two horizontal plates is analysed. An exact solution for the velocity and temperature have been obtained. the effects of Hall currents on the velocity, the temperature and shear stress are discussed analytically and graphically.With 5 Figures     

Micromagnetic simulation of domain wall pinning and domain wall motion

Domain wall pinning is the coercivity mechanism of permanent magnets used in high temperature applications. In SmCo based magnets domain walls get trapped at the cellular precipitation structure causing a high coercive field. The motion of domain walls and their propagation velocity are important in soft magnets as used in sensor applications. A finite element micromagnetic algorithm was developed to study the motion of domain walls in complex microstructures. The cellular microstructure of SmCo magnets or the cylindrical soft wires can be easily built using tetrahedral finite elements. The pinning of the domain walls has been studied for different material compositions. Attractive and repulsive domain wall pinning are observed and their behaviour for increasing thickness of the precipitation structure is explained. The motion of domains in magnetic nanowires was calculated using adaptive mesh refinement. The wall velocity strongly depends on the domain wall structure. Transverse and vortex walls have been observed and their velocity in wires of different thickness has been studied.     

Turbulent flow through a circular pipe: Resistance and heat exchange at the constant boundary temperature

In this work, problems of the velocity profile, hydraulic resistance and heat exchange at constant equal temperature on the walls, steady-state turbulent flow, and established heat exchange in a straight channel limited by coaxial circular cylinders (a circular pipe) are solved. A moving incompressible fluid is considered as the medium, its viscous and heat-conducting properties being defined not only by its physical properties, but also by stable vortex structures that are formed upon the turbulent flow and generate local anisotropy of the medium. A vector called the director is a characteristic parameter of anisotropy. Director dynamics within the flow is assigned by a separate equation. The flow region consists of two near-wall subregions, which are adjacent to solid flow boundaries. The boundary between the subregions is determined during solving the problem. A closed set of equations is formulated for the desired values (velocity, temperature), and boundary conditions are laid. The velocity profile and temperature field in the flow were obtained in form of solutions to the corresponding boundary problems. The results of solution are compared with the experimental data and empirical formulas.     

Solution of magnetohydrodynamic flow problems using the boundary element method

A boundary element solution is implemented for magnetohydrodynamic (MHD) flow problem in ducts with several geometrical cross-section with insulating walls when a uniform magnetic field is imposed perpendicular to the flow direction. The coupled velocity and induced magnetic field equations are first transformed into uncoupled inhomogeneous convection–diffusion type equations. After introducing particular solutions, only the homogeneous equations are solved by using boundary element method (BEM). The fundamental solutions of the uncoupled equations themselves (convection–diffusion type) involve the Hartmann number (M) through exponential and modified Bessel functions. Thus, it is possible to obtain results for large values of M (M≤300) using only the simplest constant boundary elements. It is found that as the Hartmann number increases, boundary layer formation starts near the walls and there is a flattening tendency for both the velocity and the induced magnetic field. Also, velocity becomes uniform at the center of the duct. These are the well-known behaviours of MHD flow. The velocity and the induced magnetic field contours are graphically visualized for several values of M and for different geometries of the duct cross-section.     

Dispersion reduction in open-channel liquid electrochromatographic columns via pressure-driven back flow

Application of electrokinetic forces to drive the mobile phase diminishes analyte dispersion in open-channel liquid chromatographic columns due to minimization of shear in the flow field. However, the retentive layer coating the inner walls of such devices slows down the average convective velocity of solute molecules in its vicinity, inherently causing dispersion of analyte bands. In this article, we explore the possibility of reducing such dispersion in electrochromatographic columns by imposing a pressure-driven back flow in the system. Analysis shows that although such a strategy introduces shear in the flow field, the overall dispersion in the mobile phase is reduced. This occurs as the streamline velocity in such a system is greater near the channel walls than that in the center of the conduit, thereby allowing fluid dispersion to counteract wall retention effects. For an optimally chosen magnitude of the back flow, hydrodynamic dispersion of any target species in the mobile phase may be shown to diminish by a factor of 3 and 10/3 in a circular tube and a parallel-plate geometry, respectively. A similar reduction in slug dispersion is also realized in rectangular conduits for all aspect ratios. In trapezoidal geometries with large wedge angles or isotropically etched profiles, this reduction factor may attain values of 10 or greater.     

Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.     

DC-RF混合等离子体温度及流场的数值计算

直流-射频(DC-RF)混合等离子体在材料合成领域有着较大的优势.为了对这种混合等离子体的特性进行分析,本文采用基于磁流体力学方程的DC-RF等离子体模型,数值分析了操作参数的改变对混合等离子体流场的影响效应.计算结果表明,直流电弧电流及工作气体流量的增加,主要使反应室中心区域处的混合等离子体轴向速度增加,并改变该区域...     

Injection of a non-Newtonian fluid through one side of a long vertical channel

Summary The problem considered here is the injection of a non-Newtonian fluid with elastic properties through one side of a long vertical channel. Using the transformations proposed by Wang and Skalak [14] for the velocity components, the basic equations governing the flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions. The effect of the non-Newtonian parameter,S, on the velocity field and heat transfer on the walls is examined carefully.     

建筑临墙开窗对室内热压通风的模拟研究

根据进风口在墙壁上开口位置的不同,建筑开窗形式分为对墙开窗、临墙开窗、单侧墙开窗.运用airpak软件针对建筑进风口形式为临墙开窗形式下的单热源室内热压通风进行了模拟研究.通过改变进出风口中心高度差及进出风口面积比来分析中和面高度、有效热量系数、通风量、速度场及温度场的变化.结果 展示了临墙开窗形式在上述两种情况下对应...